<h2>题目编号 : 116</h2>
<div style="color:#666;font-size:80%;">03 March 2006</div><br />
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<p>A row of five black square tiles is to have a number of its tiles replaced with coloured oblong tiles chosen from red (length two), green (length three), or blue (length four).</p>
<p>If red tiles are chosen there are exactly seven ways this can be done.</p>

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<p>If green tiles are chosen there are three ways.</p>

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<p>And if blue tiles are chosen there are two ways.</p>

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<p>Assuming that colours cannot be mixed there are 7 + 3 + 2 = 12 ways of replacing the black tiles in a row measuring five units in length.</p>
<p>How many different ways can the black tiles in a row measuring fifty units in length be replaced if colours cannot be mixed and at least one coloured tile must be used?</p>
<p class="info">NOTE: This is related to problem <a href="index.php?section=problems&amp;id=117">117</a>.</p>
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